In this review, the well-known Bagley–Torvik and Painlevé models (PM), which are special
kinds of differential problems of noninteger order ranks and have a significant role in …

Herein, a pure shifted Jacobi–Galerkin (SJG) method is offered for handling linear two-
dimensional space-time diffusion and telegraph equations but by considering their …

This paper describes an algorithm for obtaining approximate solutions to a variety of well-
known Lane-Emden type equations. The algorithm expands the desired solution y (x)≃ y N …

Herein, new orthogonal polynomials have been generated from shifted Chebyshev
polynomials that fulfill a given set of homogeneous boundary conditions and the necessary …

Herein, modified orthogonal polynomials are introduced. These polynomials are generated
from the second kind of shifted Chebyshev polynomials on the interval [α, β]. The operational …

This paper presents a novel numerical approach to addressing three types of high-order
singular boundary value problems. We introduce and consider three modified Chebyshev …

In this paper, we develop a novel higher-order compact finite difference scheme for solving
systems of Lane-Emden-Fowler type equations. Our method can handle these problems …

The aim of this paper is to use the second derivative of Chebyshev polynomials (SDCHPs)
as basis functions for solving linear and nonlinear boundary value problems (BVPs). Then …

A new form of basis functions structures has been constructed. These basis functions
constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of …

The paper presents a novel method that allows one to establish numerical solutions of linear
and nonlinear ordinary differential equations—with polynomial coefficients—that contain any …